PDF To CDF
Let \(X\) be a uniformly distributed random variable on the interval [1,12]. What is the value of the Cumulative Distribution Function (CDF) at 8? Please enter your answer as a decimal with two significant figures.
Since \(X\) has a uniform distribution, \(PDF_X(x)=\frac{1}{12}\) for \(x\in [1, 12]\) and 0 otherwise. \(CDF_X(x)=\Pr[X\leq x]=\sum_{k=1}^xPDF_X(k)\). Plugging in \(x=8\), we get \(CDF_X(8)=\sum_{k=1}^8\frac{1}{12}=\frac{8}{12}=\frac{2}{3}\).